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All People in Canada are the Same Age (1997)

math.toronto.edu

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Re: All People in Canada are the Same Age (1997)

#11

Post by MauranKilom »

coldtea wrote: post #6
smallnamespace wrote: post #3

Step 9 doesn't work because it introduces a third person, and so fails to demonstrate S(2)

Isn't it Step 4, which uses as a premise what the whole thing is supposed to prove? "in every group of k people, everyone has the same age" You can't use your conclusion in your assumption!

Please take a look at the principle of induction that is explained on that page.

In short: You fix k and assume that S(k) holds. If you can show that this always implies that S(k+1) holds, all you need is a base case (e.g. S(1) being true) to "recursively" prove that S(n) holds for all n >= 1 (or whatever your base case was).

Here the fault is that the induction step (proving S(k+1) from S(k)) requires k >= 2 but only specifically S(1) was proven.

Re: All People in Canada are the Same Age (1997)

#12

Post by inimino »

dlkf wrote: post #10
smallnamespace wrote: post #3

Step 9 doesn't work because it introduces a third person, and so fails to demonstrate S(2)

I don't know why you're getting downvoted, afaict 9 is the problem.

Perhaps downvoted for spoiling the problem? Some people review the comments before looking at the article.

Re: All People in Canada are the Same Age (1997)

#13

Post by dfee »

In 2003, I remember studying fallacies in English class. I literally had an outbreak of laughter during an exercise where the prompt was: “vote for me or admit you’re racist”.

It seemed so ridiculous to teenage me that such a thing could be said. In 2020 it has been said. I’m no longer falling out of my seat laughing.

Re: All People in Canada are the Same Age (1997)

#14

Post by nathanwh »

dlkf wrote: post #10
smallnamespace wrote: post #3

Step 9 doesn't work because it introduces a third person, and so fails to demonstrate S(2)

I don't know why you're getting downvoted, afaict 9 is the problem.

TFA will inform you of this though, it's intended to be a game of reasoning. Posting the answer is spoiling the fun for people who read the comments first

Re: All People in Canada are the Same Age (1997)

#16

Post by azundo »

coldtea wrote: post #6
smallnamespace wrote: post #3

Step 9 doesn't work because it introduces a third person, and so fails to demonstrate S(2)

Isn't it Step 4, which uses as a premise what the whole thing is supposed to prove? "in every group of k people, everyone has the same age" You can't use your conclusion in your assumption!

No, not quite, the conclusion is that given a group of k people where all people have the same age, then a group of k+1 people also must have the same age. Since we know that in a group of 1 all k people have the same age, then if the proof held then a group of 2 people would have the same as well, then 3, etc. This is a common tactic in induction, you make an assumption, prove that if true it implies a general result, and then give an explicit case where the assumption holds, proving the general result.

Re: All People in Canada are the Same Age (1997)

#17

Post by vages »

nathanwh wrote: post #14
dlkf wrote: post #10

Earlier quoted context omitted.

I don't know why you're getting downvoted, afaict 9 is the problem.

TFA will inform you of this though, it's intended to be a game of reasoning. Posting the answer is spoiling the fun for people who read the comments first

Why isn't there a mechanism for hiding spoilers in your comments? I came to the comments to check whether my guess was right (it wasn't), and I'm very glad for the spoiler.

Re: All People in Canada are the Same Age (1997)

#18

Post by Thorrez »

vages wrote: post #17
nathanwh wrote: post #14

Earlier quoted context omitted.

TFA will inform you of this though, it's intended to be a game of reasoning. Posting the answer is spoiling the fun for people who read the comments first

Why isn't there a mechanism for hiding spoilers in your comments? I came to the comments to check whether my guess was right (it wasn't), and I'm very glad for the spoiler.

You don't need to come to the comments to check your guess, the website lets you check your guess yourself by clicking on the step.

> See if you can figure out in which step the fallacy lies. When you think you've figured it out, click on that step and the computer will tell you whether you are correct or not, and will give an additional explanation of why that step is or isn't valid.

Re: All People in Canada are the Same Age (1997)

#20

Post by thaumasiotes »

dlkf wrote: post #10
smallnamespace wrote: post #3

Step 9 doesn't work because it introduces a third person, and so fails to demonstrate S(2)

I don't know why you're getting downvoted, afaict 9 is the problem.

There is a problem in step 9, but the problem is not related to introducing a third person. The existence of a third person makes step 9 correct.

The problem is that we establish the base cases S(0) and S(1), and then we establish the inductive step S(n) -> S(n+1) subject to the restriction that n > 1. But this proof never demonstrates that S(1) implies S(2). The proof is completely correct that S(2) implies S(3), S(3) implies S(4), and so on.

When step 9 says "Let R be someone else in G other than P or Q", the existence of a person in G other than P or Q has not been demonstrated. G is an arbitrary group of k+1 people, and the highest k for which our statement is known to be true is 1. Thus, the minimum size of G is 2, and R may not exist.

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